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%%  This file contains the bibliography of the LiDIA 1.1 Manual.
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%%  Copyright   (c)   1995   by  LiDIA-Group    
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%%  Authors: Ingrid Biehl, Thomas Papanikolaou
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\newcommand{\etalchar}[1]{$^{#1}$}
%\begin{thebibliography}{KKW{\etalchar{+}}93}
\begin{thebibliography}{KKW{\etalchar{+}}103} % MJJ

\bibitem{CAbel} C.S. Abel:
\IT{Ein Algorithmus zur berechnung der Klassenzahl und des Regulators
reellquadratischer Ordnungen}, Ph.D. thesis, Universit{\"a}t des Saarlandes,
Saarbr{\"u}cken, Germany, 1994.

\bibitem{abra} M. Abramowitz, and I.A. Stegun: 
\IT{Handbook of mathematical functions with formulas, graphs and 
mathematical tables}. National Bureau of Standards, Washington D.C., 1964

\bibitem{al-pom} W.R. Alford, and C. Pomerance:
\IT{Implementing the self initializing quadratic sieve on a distributed
network}. Manuscript, 1993

\bibitem{apostol} T.M. Apostol: 
\IT{CALCULUS}. Blaisdell Publ.~Co., 1962

\bibitem{Babai} L. Babai:
\IT{On Lov{\'{a}}sz\' lattice reduction and the nearest lattice point problem},
Combinatorica 6, 1-13, 1986.

\bibitem{BachEulerProd} E.~Bach:
\IT{Improved approximations for {E}uler products}, Unpublished MS., 1994.

\bibitem{fberger} F.-D. Berger:
\IT{Faktorisieren mit elliptischen Kurven}. Diplomarbeit, Universit\"at des
Saarlandes, 1992

\bibitem{BBQuadOrd} I.~Biehl and J.~Buchmann:
\IT{Algorithms for quadratic orders}, Proceedings of Symposium on Mathematics
of Computation, 1993.

\bibitem{boehm} H. Boehm, and M. Weiser:
\IT{Garbage collection in an uncooperative environment}, Software Practice
\& Experience, September 1988, pp. 807-820.

\bibitem{boehmh} H. Boehm:
\IT{Space efficient conservative garbage collection}, Proceedings of the ACM
SIGPLAN '91 Conference on Programming Language Design and Implementation,
SIGPLAN Notices 28, 6 (June 1993), pp. 197-206.

\bibitem{borwein} J.M. Borwein, and P.B. Borwein:
\IT{Pi and the AGM}.  Canadian Mathematical Society, Series of Monographs and
Advanced Texts, Wiley-Interscience Publication, 1987

\bibitem{brentc} R.P. Brent: 
\IT{The complexity of multiple-precision arithmetic}. Complexity 
of Computational Problem Solving (R.S.~Anderssen and R.P.~Brent 
Eds.), University of Queensland Press, 1976

\bibitem{brentj} R.P. Brent: 
\IT{Fast multiple-precision evaluation of elementary functions}. 
Journal of ACM, Vol.~23, p.~242, 1976

\bibitem{brentm} R.P. Brent:
\IT{Multiple-precision zero finding methods and the complexity of 
elementary function evaluation}. Proc.~Symp.~on Analytic Computational
Complexity, J.F.~Traub, Ed., Academic Press,  pp.~151-176, 1976

\bibitem{brente} R.P. Brent:
\IT{Some new algorithms for high-precision computation of {E}uler's 
constant}. Mathematics of Computation, Vol.~34, No.~149, p.~305, 1980

\bibitem{BuLe} J.~Buchmann, and H.W. Lenstra, Jr.:
\IT{Computing maximal orders and decomposing primes in number fields}.

\bibitem{BUK} J.~Buchmann, and V. Kessler:
\IT{Computing a lattice basis from a generating system}. preprint 1991

\bibitem{BSub} J.~Buchmann:
\IT{A subexponential algorithm for the determination of class groups and
regulators of algebraic number fields}, S\'{e}minaire de Th\'{e}orie des
Nombres (Paris), 1988-89, pp.~27--41.

\bibitem{BJTAb} J.~Buchmann, M.J. Jacobson, Jr., and E.~Teske:
\IT{On some computational problems in finite abelian groups}, to appear in
Math. Comp., 1996.

\bibitem{carlson} B.C. Carlson: 
\IT{An algorithm for computing logarithms and arctangens}. 
Mathematics of Computation, Vol.~26, No.~118, p.~543, 1972

\bibitem{cohen} H. Cohen:
\IT{A course in computational algebraic number theory}. Springer-Verlag,
1993

\bibitem{TDek} T.J. Dekker:
\IT{Point Technique for Extending the Available Precision},
Numer. Math. 18 (1971), pp. 224-242.

\bibitem{denny} T.F. Denny:
\IT{Faktorisieren mit dem Quadratischen Sieb}. Diplomarbeit,
Universit\"at des Saarlandes, 1993

\bibitem{dentzer} R. Dentzer: 
\IT{libI: Eine lange ganzzahlige Arithmetik}. Universit\"at Heidelberg, 1991

\bibitem{Dom89} P.D. Domich:
\IT{Residual {H}ermite normal form computations}.  ACM Transactions on
Mathematical Software, Vol.~15, no.~3, pp.~275-286, 1989

\bibitem{Due91} S. D\"ullmann:
\IT{Ein Algorithmus zur Bestimmung der Klassengruppe positiv definiter
bin\"arer quadratischer Formen}.  {Dissertation, Universit\"at des Saarlandes},
{1991}

\bibitem{eckel} B. Eckel:
\IT{Using C++}. Osborne McGraw-Hill, 1989

\bibitem{eirund} H. Eirund:
\IT{Objektorientierte Programmierung}. Leitf\"aden der angewandten 
Informatik, Teubner, 1993

\bibitem{FiP} U. Fincke, and M. Pohst:
\IT{Improved methods for calculation vectors of short length in a lattice,
including a complexity analysis.}
Math.\ Comp.\ 44, 463--471 (1985).

\bibitem{forster} O. Forster:
\IT{Analysis I}. Vieweg Verlag, 1983 

\bibitem{FWQuadPoly} G.W. Fung and H.C. Williams:
\IT{Quadratic polynomials which have a high density of prime values}, Math.
Comp. {\bf 55} (1990), 345--353.

\bibitem{gnump} T. Granlund:
\IT{The GNU multiple precision arithmetic library}, Free Software
Foundation Inc., Cambridge, 1993

\bibitem{HMSub} J.L. Hafner and K.S. McCurley:
\IT{A rigorous subexponential algorithm for computation of class groups},
Tech. report, IBM Research Report, San Jose, CA, 1989.

\bibitem{HLConF} G.H. Hardy and J.E. Littlewood:
\IT{\em Partitio numerorum {III}: On the expression of a number as a sum of
primes}, Acta Math. {\bf 44} (1923), 1--70.

\bibitem{HaHoRe93} G. Havas, D.F. Holt, and S. Rees:
\IT{Recognizing badly presented $\Z$-modules}.
{in: Linear Algebra and its Applications},
{Vol.~192},
{1993},
{pp.~137-163}   

\bibitem{HaMa94} G. Havas, and B.S. Majewski:
\IT{Integer matrix diagonalization}.
{Key Centre for Software Technology, Department of
Computer Science, The University of Queensland},
{TR0277},
{1994}

\bibitem{HaSter79} G. Havas, and  L.S. Sterling:
\IT{Integer matrices and Abelian groups}.
Springer-Verlag, {Lecture Notes in Computer Science 72},
{1979}

\bibitem{IEE87} IEEE: \IT{IEEE standard 754-1985 for binary 
floating-point arithmetic}.  reprinted in SIGPLAN 22, 2:9-25, 1987

\bibitem{JLWNumEx} M.J. Jacobson, Jr., R.F. Lukes, and H.C. Williams:
\IT{An investigation of bounds for the regulator of quadratic fields},
Experimental Mathematics {\bf 4} (1995), no.~3, 211--225.

\bibitem{JSieve} M.J. Jacobson, Jr.:
\IT{Computing quadratic class groups via sieving},
Unpublished manuscript (1997).

\bibitem{kern} B.W. Kernigham, and D.M. Ritchie: 
\IT{Programmieren in C}. Carl Hanser Verlag, 1983 

\bibitem{kkwlr} R. Klatte, U. Kulisch, A. Wiethoff, C. Lawo, and M.~Rauch:
\IT{C-{XSC} A C++ class library for extended scientific computing}.
Springer-Verlag, 1993

\bibitem{knuth} D.E. Knuth: 
\IT{The art of computer programming}. Addison--Wesley Co., 
Inc., Vol.~2, 1980

\bibitem{koenig} A. K\"onig:
\IT{Der C-Experte: Programmieren ohne Panne}.
Addison--Wesley Publishing Company Inc., Reading, 1989

\bibitem{lenstra} A.K. Lenstra: 
\IT{lip: long integer package}. Bellcore, 1989

\bibitem{LAK} A.K. Lenstra, H.W. Lenstra, Jr., and L. Lov{\'{a}}sz:
\IT{Factoring polynomials with rational coefficients}.
Mathematische Annalen 261, pp.~515-534, 1982

\bibitem{Lcalculation} H.W. Lenstra, Jr.:
\IT{On the calculation of regulators and class numbers of quadratic fields},
London Math. Soc. Lecture Note Series {\bf 56} (1982), 123--150.

\bibitem{lenstra_ecm} H.W. Lenstra,~Jr.:
\IT{Factoring integers with elliptic curves}.
Annals of Mathematics 126, pp.~649-673, 1987

\bibitem{Linna} S. Linnainmaa:
\IT{Software for doubled-precision floating point computations},
ACM TOMS 7, 172-283 (1081).

\bibitem{lippman} S.B. Lippman:
\IT{C++ Primer}.
Addison-Wesley Publishing Company, 1989, 
Reprinted with corrections March, 1990

\bibitem{Lclassnumber} J.E. Littlewood:
\IT{On the class number of the corpus ${P}(\surd - k)$}, Proc. London Math.
Soc. {\bf 27} (1928), 358--372.

\bibitem{mersch} P. Merscher: 
\IT{Standards f\"ur objektorientiertes Programmieren in der 
Computeralgebra}. Diplomarbeit, Universit\"at des Saarlandes, 1992

\bibitem{MWComph} R.A. Mollin and H.C. Williams:
\IT{Computation of the class number of a real quadratic field},
Utilitas Mathematica {\bf 41} (1992), 259--308.

\bibitem{Mueller94} Achim M\"uller:
\IT{Effiziente Algorithmen f\"ur Probleme der linearen Algebra \"uber $\Z$}.
{Diplomarbeit, Universit\"at des Saarlandes},
{1994}

\bibitem{amueller} Andreas M\"uller:
\IT{Eine FFT-Continuation f\"ur die Elliptische Kurven Methode}.
Diplomarbeit, Universit\"at des Saarlandes,  in preparation.

\bibitem{perron} O. Perron: 
\IT{Die Lehre von den Kettenbr\"uchen I, II}. B.G.~Teubner, 
Stuttgart, 1977 

\bibitem{Pfahler96} T. Pfahler:
\IT{Polynomfaktorisierung \"uber endlichen K\"orpern}.
{Diplomarbeit, Universit\"at des Saarlandes},
{1996}

\bibitem{pohl} I. Pohl:
\IT{C++ for C programmers}.
The Benjamin/Cummings Publishing Company, Inc., 1989

\bibitem{pom_qs} C. Pomerance:
\IT{Analysis and comparison of some integer factoring algorithms}.
Computational Methods in Number Theory (H.W. Lenstra, Jr. and R.~Tijdeman,
eds.), Math. Centrum Tracts, Amsterdam, 1983, Number 155, Part II,
pp.~235--286.

\bibitem{ZAS} M. Pohst, and H. Zassenhaus:
\IT{Algorithmic algebraic number theory}.  Encyclopedia of Mathematics and its
Applications, Cambridge University Press, 1989

\bibitem{DPri} D. Priest:
\IT{On properties of floating point arithmetics: numerical stability
and the cost of accurate computations}, Ph.D. Diss, Berkeley 1992.

\bibitem{rama} S. Ramanujan: 
\IT{Collected papers of {S}rinivasa {R}amanujan}. Cambridge University Press,
1927 

\bibitem{SEN} C.P. Schnorr, and M. Euchner:
\IT{Lattice basis reduction:  improved practical algorithms and solving subset
sum problems}.  Proceedings of the FCT 91, p.~68-85, 1991

\bibitem{SchQuad} R.J. Schoof:
\IT{Quadratic fields and factorization}, Computational Methods in Number
Theory (H.W. Lenstra, Jr. and R.~Tijdeman, eds.), Math. Centrum Tracts,
Amsterdam, 1983, Number 155, Part II, pp.~235--286.

\bibitem{shanks} D. Shanks, and J.W. Wrench: 
\IT{The calculation of $\pi$ to 100,000 decimals}. Mathematics of Computation,
Vol.~16, p.~76, 1962 

\bibitem{Sclass} D.~Shanks:
\IT{Class number, a theory of factorization and genera}, Proc.  Symp. Pure
Math. 20, AMS, Providence, R.I., 1971, pp.~415--440.

\bibitem{ShLitBounds} \bysame:
\IT{Systematic examination of {L}ittlewood's bounds on ${L}(1,\chi)$},
Proc. Sympos. Pure Math, AMS, Providence, R.I., 1973, pp.~267--283.

\bibitem{ShoupGF} V. Shoup:
\IT{A new polynomial factorization algorithm and its implementation}.
Universit\"at des Saarlandes, 1994

\bibitem{sosnow} T. Sosnowski: 
\IT{Faktorisieren mit dem Quadratischen Sieb auf dem Hypercube}.
Diplomarbeit, Universit\"at des Saarlandes, 1994 

\bibitem{stoer} J. Stoer: 
\IT{Einf\"uhrung in die numerische Mathematik I}. Springer-Verlag, 
1983 

\bibitem{stroustrup} M.A. Stroustrup, and B. Ellis:
\IT{The annotated C++ reference manual}.
Addison--Wesley Publishing Company, Reading,  1990, 
ANSI Base Document

\bibitem{sweeny} D.W. Sweeny: 
\IT{On the computation of {E}uler's constant}. Mathematics of Computation,
Vol.~15, 1961 

\bibitem{unixc} UNIX System Laboratories, London, England:
\IT{C++ language system release 3.0.1}. 1992, Release Notes

\bibitem{unixcc} UNIX System Laboratories, London, England:
\IT{C++ language system release 3.0.1}. 1992, Selected Readings

\bibitem{GathenShoup} J. von~zur~Gathen, and V. Shoup:
\IT{Computing {F}robenius maps and factoring polynomials}.
Computational Complexity, 2:187-224, 1992

\bibitem{watson} G.N. Watson: 
\IT{A treatise on the theory of {B}essel functions}. 2nd ed., 
Cambridge University Press, 1944 

\bibitem{BEW} B. de~Weger:
\IT{Algorithms for {D}iophantine approximation}. 
Thesis, Centrum voor Wiskunde en Informatica (CWI), pp.~49-51, 1987

\bibitem{new} S. Wetzel, W. Backes, and T. Lauer:
\IT{Some practical results on lattice reduction algorithms.} In 
preparation.

\end{thebibliography}
